Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
3342 conjugacy classes of subgroups; only the 675 normal subgroups are shown.
This group has 3342 conjugacy classes of subgroups — too many to draw. Only its 675 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#16810524 | C2 | semidirect |
| 3. C2×C42×Dic53 | C2 | semidirect |
| 4. C2×C53×#384 | C2 | semidirect |
| 8. C2×#13133214 | C4 | semidirect |
| 27. C2×C4×Dic53 | D4 | semidirect |
| 57. C42×C53 | C22⋊C4 | semidirect |
| 81. C2×Dic53 | #127 | semidirect |
| 97. C4×C53 | #390 | semidirect |
| 101. C2×#384 | D53 | semidirect |
| 120. C53 | #14713 | semidirect |
| 164. C42 | #11719921 | semidirect |
| 202. C4 | #16810524 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133214 | 2 |
| C2×#16810524 | 2 |
| C2×C42×Dic53 | 2 |
| C2×C53×#384 | 2 |
| #14713 | 53 |